perplexus.info :: Just Math : Seems unlikely, but is not …

Seems unlikely, but is not … (Posted on 2023-04-06)

Find two distinct numbers, so that
x^2-y=91
y^2-x=91

No Solution Yet Submitted by Ady TZIDON

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Puzzle Solution

| Comment 1 of 3

x^2-y=91. .....(I)

y^2-x =91.....(iii)

Subtracting (ii) from (I), we have:

x^2-y^2-(y-x) =0

--> (x-y)(x+y+1)=0

--> x+y=-1, since x is not equal to y.

--> y =--1-x

Then, from x^2-y=91, we have:

x^2 - (-1-x) =91

x^2+x= 90

--> (x+10)(x-9) =0

x= -10,9

If x=--10, then: y = -1+10 =9

If x= 9, then, y = -1-9=-10

Edited on April 6, 2023, 10:33 am

Posted by K Sengupta on 2023-04-06 08:10:08

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